# calculus and maximum and minimum values

Feb 3rd, 2012
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Career Point College - Tulsa
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Use the definition to derive the formula for the derivative Find all the horizontal and vertical asymptotes of the graph of maximum and minimum values

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(1)Differentiating with respect to (2)Differentiating with respect to since (3)Differentiating with respect to (4)Let Since (5)We have (6)Therefore, the maximum is 20 and minimum is 17(7)Therefore, the maximum is and minimum is (8)The velocity function is the derivative of the position function.The acceleration is the derivative of the velocity function. (9)The velocity function is the derivative of the position function.The acceleration is the derivative of the velocity function. (10)Differentiating with respect to The tangent equation is at (11)Differentiating with respect to The tangent equation is at (12)Differentiating with respect to And the point is So slope and point form: (13)Therefore, the line is a horizontal asymptote.Since denominator is zero when Therefore, the lines are vertical asymptote.(14)By L'Hospital's rule: (15)By L'Hospital's rule: Again by L'Hospital's rule(16)By L'Hospital's rule: Again by L'Hospital's rule(17)Differentiating with respect (18)Differentiating with respect At the point Point and slope form : (19)Volume of the cone is,Given that,Substitute in (1), we getNow substitute, andin (2), we getTherefore the height of the cone is increasing at the rate of(20)Consider The velocity function is the derivative of the position function.The object is moving to the l

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